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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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B. 12

(x-12) (x+8) so solutions are 12, -8
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2$$ − $$4x$$ = $$96$$

Or, $$x^2$$ − $$4x$$ − $$96$$ = 0

Or, $$x^2$$ $$−12x$$ + $$8x$$ − $$96$$ = 0

Or, x ( x - 12 ) + 8 ( x - 12 ) = 0

Or x = 12 , -8

So , The larger of the 2 solutions must be (B) 12

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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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Solving Quadratic equation $$x^2 − 4x = 96$$

$$x^2 - 4x - 96 = 0$$

$$x^2 - 12x - 8x - 96 = 0$$

x (x - 12) + 8 (x - 12) = 0

(x + 8) (x - 12)

x = 12, -8

x=12 is larger value

Therefore Answer is B......

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GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23 Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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Simply set the quadratic equation to zero and factor the roots out.

$${ x }^{ 2 }-4x=96\\ { x }^{ 2 }-4x-96=0\\ \left( x+8 \right) \left( x-12 \right) =0\\ x=-8,\quad x=12$$

For those people, like me, who struggle to find the roots, I suggest using one approach I took from pacifist85.

Prime factorize the constant and see which number combinations that sum to 4 and multiply to 96.

$$96={ 2 }^{ 5 }\ast { 3 }^{ 1 }$$

You will eventually find the 8 and 12 roots.
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2 − 4x = 96$$

Or, $$x^2 − 4x − 96 = 0$$

Or, $$x^2 − x ( 12 − 8 ) − 96 = 0$$

Or, $$x^2 − 12x + 8x − 96 = 0$$

Or, $$x ( x − 12 ) + 8( x − 12 ) = 0$$

So, $$x = 12$$ , $$− 8$$

Thus, larger of the 2 numbers is 12 , answer must be (B) 12
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

$$x^2 - 4x - 96 = 0$$
$$x^2 - 4x + 4 - 100 = 0$$
$$(x-2)^2 = 100$$
$$x-2 = 10$$ or $$x-2 = -10$$
roots are 12 and -8, with 12 being the larger. => Answer B
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GMAT 1: 720 Q48 V40 Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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The solution should be one of the roots of x^2−4x−96=0

Working from the answer choices, we can work backwards to see if we get an integer quotient by dividing 96 by the answer choice and then checking if we can get a -4 as the difference between the quotient and the answer choice.

Only B fits the scenarios as 96/12 = 8 and 12-8 is 4.
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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I have a question here. So in the equation given : x^2 - 4x =96 then x(x-4)=96 therefore x=96 or x-4=96 x=100
I know for the fact that this method is incorrect. But am not understanding why is it incorrect. can someone please help me
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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x^2−4x=96 => (x-12)*(x+8) = 0. > x = 12 or x = -8 => answer B
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

Let’s solve the given quadratic:

x^2 - 4x - 96 = 0

(x + 8)(x - 12) = 0

x = -8 or x = 12

The larger of the two solutions is 12.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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Solving for quadratic is definitely the fastest route to an answer on this one but one could also simply test answer choices in a relatively fast manner as well w/o actually having to do much math (either start from E given we are looking for the "larger" of two solutions or use the optimal B/D approach)

E) 100^2 - 4(100) = 96 --> clearly doesn't work (recognize here that the x^2 needs to be a lot smaller)
D) 32^2 - 4(32) = 96 --> same rationale as above (x^2 still too big)
C) 16^2 - 4(16) = 96 --> x^2 still too big but getting closer...
B) 12^2 - 4(12) = 96 --> looks promising so do a quick check...144 - 48 = 96 --> correct answer choice

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2 − 4x - 96 = 0$$

Or, $$x^2 − 12x +8x - 96 = 0$$

Or, $$x(x - 12) +8( x - 12) = 0$$

Either x = -8 or x = 12, Thus Answer must be (B)
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Thanks and Regards

Abhishek....

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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(x-12)(x+8)=0
x=12, x=-8
So larger solution is 12

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

It might take a few attempts to know the two factors that once multiplied result in 96

We can choose from the answer choices

16 and 12 have a difference of 4 but will definitely have a multiple larger than 96.

So it is between 12 and 8 then it must be 12.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?  [#permalink]

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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

x^2-12x*8x-96=0
(x-12)(x+8)=0
x = 12 or -8
Larger solution = 12

IMO B

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